The Decibel Subjects Covered The bel and decibel units Relative Power Gain Relative Voltage Gain dBm and Absolute Power Gain The bel and decibel units Derived from how a received signal is perceived Specifically by the human ear It, the human ear, is logarithmic not linear With two sounds, one perceived as being twice as loud The louder sound actually has approx. four times the power The original unit, the bel, was name in honor of Alexander Graham Bell the decibel = 1/10 bels and is the most commonly used unit

The Decibel Relative Power Gain Relative Power Gain = (Power Output)/(Power Input) A p = P o /P i Where P o & P i are specified in Watts The gain can be the same for different values of P o & P i Usually expressed in terms of Decibels {A P(dB) } A P(dB) = 10 log A p or A P(dB) = 10 log (P o /P i ) Example Problems dB.1 Given: Amplifier with Po = 2.75W & Pi = 50 mW Find: A p & A P(dB) dB.2 -- Second page of the handout

The Decibel Relative Power Gain Finding Gain from Gain measured in dBs Example Problems dB.4 -- Third Page of the handout Relative Voltage Gain Review of Logarithms Fire up the PCs, Click Start, Click Run, Type calc in the text box Click View Tab, Click Scientific Enter the following numbers click log button & record results 10, 100, 1000, 10000

The Decibel Relative Voltage Gain Review of Logarithms Enter 10, the x^y button, the following numbers and record 1, 2, 3, 4 Compare the two sets of results Conclusions????????? Derivation P o = V 0 2 /R 0 and P i = V i 2 /R i A P(dB) = 10 log (P o /P i ) = 10log (V 0 2 /R 0 )/(V i 2 /R i ) If R 0 and R i are equal then they cancel each other = 10 log {(V 0 2 /R)/(V i 2 /R )} = 10 log{(V 0 2 )/(V i 2 )} = 10 log{(V 0 )/(V i )} 2 A V(dB) = 20 log V 0 / V i = 20 log A v where A v = V 0 / V i

The Decibel Relative Voltage Gain Derivation Reverse Av = 10 AV(dB)/20 = V 0 / V i Example Problems 2.5 and 2.6 Fourth page of the handout Questions Absolute Power Gain and dBm Previous discussion of dBs were relative measures i.e, an infinite sets of powers that can yield a 10 dB change

The Decibel Absolute Power Gain and dBm Communications industry developed a standard Load resistance from the set 50  s, 600  s, or 900  s Reference power level = 1 mW Symbol = dBm Formulas A P(dBm) = 10log P/(1mW) Reverse P = 1 mW (10 AP(dBm)/10 ) Example Problems 2.7 and 2.8

The Decibel Common Decibel Relationships